Average Error: 0.1 → 0.1
Time: 5.4s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + \left(y \cdot \log \left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) + y \cdot \log \left(\sqrt[3]{\sqrt[3]{z}}\right)\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + \left(\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + \left(y \cdot \log \left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) + y \cdot \log \left(\sqrt[3]{\sqrt[3]{z}}\right)\right)\right)
double f(double x, double y, double z) {
        double r334018 = x;
        double r334019 = 0.5;
        double r334020 = r334018 * r334019;
        double r334021 = y;
        double r334022 = 1.0;
        double r334023 = z;
        double r334024 = r334022 - r334023;
        double r334025 = log(r334023);
        double r334026 = r334024 + r334025;
        double r334027 = r334021 * r334026;
        double r334028 = r334020 + r334027;
        return r334028;
}
↓
double f(double x, double y, double z) {
        double r334029 = x;
        double r334030 = 0.5;
        double r334031 = r334029 * r334030;
        double r334032 = 1.0;
        double r334033 = z;
        double r334034 = 2.0;
        double r334035 = cbrt(r334033);
        double r334036 = log(r334035);
        double r334037 = r334034 * r334036;
        double r334038 = r334033 - r334037;
        double r334039 = r334032 - r334038;
        double r334040 = y;
        double r334041 = r334039 * r334040;
        double r334042 = r334035 * r334035;
        double r334043 = cbrt(r334042);
        double r334044 = log(r334043);
        double r334045 = r334040 * r334044;
        double r334046 = cbrt(r334035);
        double r334047 = log(r334046);
        double r334048 = r334040 * r334047;
        double r334049 = r334045 + r334048;
        double r334050 = r334041 + r334049;
        double r334051 = r334031 + r334050;
        return r334051;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[\left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right)\]

Derivation

  1. Initial program 0.1

    \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.1

    \[\leadsto x \cdot 0.5 + \color{blue}{\left(y \cdot \left(1 - z\right) + y \cdot \log z\right)}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.1

    \[\leadsto x \cdot 0.5 + \left(y \cdot \left(1 - z\right) + y \cdot \log \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)}\right)\]

  6. Applied log-prod0.1

    \[\leadsto x \cdot 0.5 + \left(y \cdot \left(1 - z\right) + y \cdot \color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)}\right)\]

  7. Applied distribute-lft-in0.1

    \[\leadsto x \cdot 0.5 + \left(y \cdot \left(1 - z\right) + \color{blue}{\left(y \cdot \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)}\right)\]

  8. Applied associate-+r+0.1

    \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(y \cdot \left(1 - z\right) + y \cdot \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)}\]

  9. Simplified0.1

    \[\leadsto x \cdot 0.5 + \left(\color{blue}{\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y} + y \cdot \log \left(\sqrt[3]{z}\right)\right)\]
  10. Using strategy rm

  11. Applied add-cube-cbrt0.1

    \[\leadsto x \cdot 0.5 + \left(\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + y \cdot \log \left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\right)\right)\]

  12. Applied cbrt-prod0.1

    \[\leadsto x \cdot 0.5 + \left(\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + y \cdot \log \color{blue}{\left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right)}\right)\]

  13. Applied log-prod0.1

    \[\leadsto x \cdot 0.5 + \left(\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + y \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) + \log \left(\sqrt[3]{\sqrt[3]{z}}\right)\right)}\right)\]

  14. Applied distribute-lft-in0.1

    \[\leadsto x \cdot 0.5 + \left(\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + \color{blue}{\left(y \cdot \log \left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) + y \cdot \log \left(\sqrt[3]{\sqrt[3]{z}}\right)\right)}\right)\]

  15. Final simplification0.1

    \[\leadsto x \cdot 0.5 + \left(\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + \left(y \cdot \log \left(\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) + y \cdot \log \left(\sqrt[3]{\sqrt[3]{z}}\right)\right)\right)\]

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

  :herbie-target
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

  (+ (* x 0.5) (* y (+ (- 1 z) (log z)))))